The motion is scheduled to be brought before parliament in a preliminary vote on Wednesday.
Mr Netanyahu, leader of the right-wing Likud party, is now on trial on corruption charges.
Netanyahu has been charged with fraud, breach of trust and accepting bribes in a series of scandals in which he is accused of offering favors to wealthy media figures in exchange for positive news coverage about him and his family.
Opinion polls predict that Netanyahu's Likud Party would still emerge as the largest party in parliament in the next election, but with far fewer seats than it now has.
Opposition leader Yair Lapid, whose Yesh Atid party voted in favour of new elections, accused the government of gross mishandling of the coronavirus crisis and its economic fallout.
Wednesday's vote on an opposition-backed measure is however preliminary.
Under the coalition deal, Netanyahu is to serve as prime minister until November 2021, with the job rotating to Gantz for 18 months after that.
"I joined this government with a heavy but whole heart" after a third inconclusive election in March, Defense Minister Benny Gantz told a news conference.
Israel is still operating on a version of the 2019 budget which was approved in 2018.
Israeli Prime Minister Benjamin Netanyahu on Monday said he opposed attempts to call for new elections and urged his coalition partners to keep the current power-sharing government.
The Netanyahu-Gantz coalition, agreed in April, included strict power-sharing arrangements, with cabinet posts split roughly evenly between allies of both men.
Gantz appears to have concluded that elections are inevitable and the sooner they are held the better. Blue and White then announced on Tuesday that it would also vote with the opposition.
The decision does not automatically mean the country will head to its fourth national election in the past two years, as the legislation now goes to a parliamentary committee for discussion and possible modification before coming back to the house for the required second and third readings expected next week.
At the same time, he cracked open an opportunity for Netanyahu to avert the collapse of their coalition, telling him all he had to do was pass a 2020 budget by a December 23 deadline and get the government functioning again.
"Netanyahu didn't lie to me", Gantz said.
The delayed 2021 budget includes key reforms aimed at helping the Israeli economy recover from the coronavirus pandemic.
"Infection rates are increasing again".
"If there's a budget and a functioning government, then we're in", Gantz said. The lack of budget has caused severe hardships and cutbacks for Israelis at a time when unemployment is estimated at more than 20 per cent because of the coronavirus outbreak.